Section 1.1, Slide 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 13.2, Slide 1 13 Probability What Are the Chances?

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 13.2, Slide 2 Complements and Unions of Events 13.2 Understand the relationship between the probability of an event and the probability of its complement. Calculate the probability of the union of two events.

Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 13.2, Slide 3 Complements and Unions of Events 13.2 Use complement and union formulas to compute the probability of an event.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 13.2, Slide 4 Complements of Events

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 13.2, Slide 5 Example: The graph shows the party affiliation of a group of voters. If we randomly select a person from this group, what is the probability that the person has a party affiliation? Complements of Events (continued on next slide)

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 13.2, Slide 6 Solution: Let A be the event that the person we select has some party affiliation. It is simpler to calculate the probability of A'. Since 23.7% have no party affiliation, Complements of Events P(A) = 1 – P(A') = 1 – =

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 13.2, Slide 7 Unions of Events

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 13.2, Slide 8 Example: If we select a single card from a standard 52-card deck, what is the probability that we draw either a heart or a face card? Solution : Let H be the event “draw a heart” and F be the event “draw a face card.” We are looking for P(H U F). Unions of Events (continued on next slide)

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 13.2, Slide 9 Unions of Events There are 13 hearts, 12 face cards, and 3 cards that are both hearts and face cards.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 13.2, Slide 10 Unions of Events

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 13.2, Slide 11 Example: A survey found that 35% of a group of people were concerned with improving their cardiovascular fitness and 55% wanted to lose weight. Also, 70% are concerned with either improving their cardiovascular fitness or losing weight. If a person is randomly selected from the group, what is the probability that the person is concerned with both improving cardiovascular fitness and losing weight? Unions of Events (continued on next slide)

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 13.2, Slide 12 Solution: Let C be the event “the person wants to improve cardiovascular fitness” and W be the event “the person wishes to lose weight.” We need to find P(C ∩ W). We have P(C) = 0.35, P(W) = 0.55, and P(C U W) = Unions of Events

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 13.2, Slide 13 Example: A survey of consumers shows the amount of time they spend shopping on the Internet per month compared to their annual income (see next slide). If we select a consumer randomly, what is the probability that the consumer neither shops on the Internet 10 or more hours per month nor has an annual income above $60,000? Combining Complement and Union Formulas (continued on next slide)

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 13.2, Slide 14 Solution: Let T be the event “the consumer selected spends 10 or more hours per month shopping on the Internet.” Let A be the event “the consumer selected has an annual income above $60,000.” Combining Complement and Union Formulas (continued on next slide)

Copyright © 2014, 2010, 2007 Pearson Education, Inc.Section 13.2, Slide 15 Combining Complement and Union Formulas From the table we get n(T) = = 480 and n(A) = = 496. With n(S) = 1,600, we may compute the probabilities below.